The equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.
The circle x^2 + y^21 = 36 is centered at (0, 0) and has a radius 6.
x^2 + y^2 + 2x = 35
=> x^2 + 2x + 1 + y^2 = 36
=> (x + 1)^2 + y^2 = 36
This is a circle centered at (-1, 0) and has a radius 6. As the center of the circles are at a distance of 1 and their radius is equal the two intersect each other.
The circles x^2 + y^2 = 36 and x^2 + y^2 + 2x = 35 intersect each other